The magnitudes of mutually perpendicular forces a,b and c are 2,10 and 11 respectively. Then the magnitude of its resultant is

Options

A. 12
B. 15
C. 9
D. none of these

Explanation

To find the magnitude of the resultant of three mutually perpendicular forces \( a, b, \) and \( c \) with magnitudes 2, 10, and 11 respectively, we can follow these steps:

### Step 1: Identify the Magnitudes
The magnitudes of the forces are given as:
- \( |a| = 2 \)
- \( |b| = 10 \)
- \( |c| = 11 \)

### Step 2: Use the Formula for Resultant of Perpendicular Vectors
For three mutually perpendicular vectors, the magnitude of the resultant \( R \) can be calculated using the formula:
\[ R = \sqrt{|a|^2 + |b|^2 + |c|^2} \]

### Step 3: Substitute the Values
Substituting the values of the magnitudes into the formula:
\[ R = \sqrt{2^2 + 10^2 + 11^2} \]

### Step 4: Calculate Each Square
Now, calculate the squares of each magnitude:
- \( 2^2 = 4 \)
- \( 10^2 = 100 \)
- \( 11^2 = 121 \)

### Step 5: Sum the Squares
Now, add these squared values together:
\[ R = \sqrt{4 + 100 + 121} \]
\[ R = \sqrt{225} \]

### Step 6: Calculate the Square Root
Finally, calculate the square root of 225:
\[ R = 15 \]

### Conclusion
The magnitude of the resultant of the three mutually perpendicular forces is \( 15 \).

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